Most commonly prescribed antidepressants are SSRIs and SNRIs. They increase the levels of a chemical called Serotonin in your brain which is a neurotransmitter that "might be responsible" for "transmitting positive feelings of well being". However, the connection between Serotonin deficiency and anxiety and depression is not a scientifically proven fact. There are NO scientific research papers (academic, peer-reviewed) out there that prove this except for some pseudo-science propaganda funded by big pharma. No self-respecting academic neuroscientist will stand behind this theory.
There is just drug statistics that show that about 25% of patients benefit from antidepressants which is about the same as number of patients who took placebo during tests. Antidepressants are just as good as placebo. Between 30% and 50% of people treated with antidepressants do not show a response at all! It's the pharmaceutical industry that turned this into "a fact" through campaigns and advertising and manipulation or outright bribery to push their drugs, to the point that many doctors present this to you as a fact, which is not true.
According to NIH about the same number of patients improve spontaneously or through therapy, assuming they don't have any other underlying issues that cause depression and anxiety. Also, Serotonin levels vary between areas of the brain. Antidepressants increase serotonin levels globally or even randomly which may cause various reaction among different people depending on their pre-existing Serotonin levels.
A person with Aspergers, or any person for that matter, may have normal Serotonin levels and that's what makes them super-sensitive to drugs that increase Serotonin levels. Because increasing the levels of Serotonin will make you feel sick too: hyperactive, edgy, headaches, confusion, insomnia, hypersensitivity to stimuli and pain it might lead to burnout, exhaustion, fast heartbeat and... anxiety, duh..., it might even lead to Serotonin Irritation Syndrome (SIS). Then you need to have your Serotonin levels lowered quickly or you will die.
So, if you're within that 25% of people who respond positively to them these drugs actually can make you feel better. Just don't believe that hype surrounding them since they don't work for most people. None of them worked for me though. I either didn't respond at all or had exaggerated, unbearable side effects and/or they made my anxiety and depression even worse. One screwed me up so badly I had to stay home for a month to recover. I've tried over 10 drugs over the last 5+ years.